# st: Negative Hausman value?

 From "Pavlos C. Symeou" To Subject st: Negative Hausman value? Date Mon, 16 Oct 2006 11:57:53 +0100

Dear Statalisters,

I attempt to compare between FE and RE transformations in Stata using the
hausman command, yet the chi^2 for the test is negative (how can a square be
negative?). I provide below the commands that I use to estimate the models,
store the model's estimates and compare them with hausman. Stata produces a
note with the output which states that the differenced variance matrix does
not equal the number of coefficients being tested. I have noticed that in
the output provided below and used in the calculations of the hausman test,
the yearly dummy "_Iyear_2004" is not included. Please bear in mind that
this yearly dummy is dropped in the initial FE and RE model estimations
because of collinearity.

I hope this helps previous threads to understand why we encounter negative
values in the hausman test.

xi: xtreg f m lagm m2 lib_fixed lib_mobile t d1-d24 i.year, fe
est store fe
xi: xtreg f m lagm m2 lib_fixed lib_mobile t d1-d24 i.year, re
hausman fe .

Note: the rank of the differenced variance matrix (52) does not equal the
number of coefficients being tested (53); be sure this is what you expect,
or there may be problems computing the test.  Examine the output of your
estimators for anything unexpected and possibly consider scaling your
variables so that the coefficients
are on a similar scale.

---- Coefficients ----
(b)          	(B)            	(b-B)
sqrt(diag(V_b-V_B))
fe           	.          		Difference
S.E.

m     		4.126995     	4.210606       	-.0836103
.
lagm    		-3.659119    	-3.719283         .060164
.
m2    		-.0035987    	-.0037695     	.0001707               .
lib_fixed    	-.7893976    	-.6248966        	-.164501
.
lib_mobile     	.8347247     .	8552306        	-.020506               .
t     		.1057887     	.0839587          	.02183
.
d1     		1.591341     1.425241        	.1661004               .
d2      		1.73248     1.566447        	.1660332
.
d3      		1.33496     1.175148        	.1598117
.
d4     		1.163786     1.009243       	 .1545424               .
d5     		1.130861     .9795363      	  .1513244               .
d6      		1.53821     1.372196        	.1660132
.
d7     		1.787398     1.618786        	.1686119               .
d8     		2.030746     1.871618        	.1591281               .
d9     		2.329689     2.175233       	 .1544567               .
d10     		2.474566     2.379384        	.0951821
.
d11     		2.530941     2.391151        	.1397903
.
d12     		2.702182     2.548153         	.154029
.
d13     		3.072654     2.923146       	 .1495087
.
d14     		3.200262     3.048934        	.1513281
.
d15     		3.434791     3.299563        	.1352286
.
d16     		4.161894     4.040091        	 .121803
.
d17     		4.693086     4.604569       	 .0885171
.
d18     		4.813464     4.765931       	 .0475332
.
d19     		4.874817     4.829945        	.0448717
.
d20     		4.763858     4.696174       	 .0676834
.
d21     		4.007245     3.914138        	.0931068
.
d22      		3.38889     3.261472       	 .1274171
.
d23     		2.073858     1.891516       	 .1823422
.
d24     		2.133198      1.90412       	 .2290783
.
_Iyear_1981     .1057826     .1715391      	 -.0657565               .
_Iyear_1982      .429569     .5114474    	 	  -.0818784
.
_Iyear_1983      .779513     .8763522    		   -.0968392
.
_Iyear_1984     1.270724     1.382196     	  -.1114715               .
_Iyear_1985     1.598364     1.731791      	 -.1334276               .
_Iyear_1986     1.724753      1.88993      	 -.1651769               .
_Iyear_1987     2.117019     2.295973      	 -.1789541               .
_Iyear_1988     2.463715     2.660981       	-.1972662               .
_Iyear_1989     2.808268     3.025018        	 -.21675               .
_Iyear_1990     3.237237     3.452751      	 -.2155147               .
_Iyear_1991     3.653473     3.891927       	-.2384541               .
_Iyear_1992     4.006215     4.272213     	  -.2659985               .
_Iyear_1993     4.307211     4.585079      	 -.2778678               .
_Iyear_1994     4.561733     4.852067      	 -.2903343               .
_Iyear_1995     4.596097     4.878367     	  -.2822704               .
_Iyear_1996     4.680343     4.956875      	 -.2765316               .
_Iyear_1997     4.754712     4.997591      	  -.242879               .
_Iyear_1998     4.427386       4.6229        	-.195514               .
_Iyear_1999     3.808497      3.95841       	-.1499126               .
_Iyear_2000     3.243333     3.354241       	 -.110908               .
_Iyear_2001     2.610181     2.692871      	 -.0826899               .
_Iyear_2002     1.963031     2.033931     	  -.0708998               .
_Iyear_2003     1.108533      1.15696       	-.0484275               .

b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg

Test:  Ho:  difference in coefficients not systematic

chi2(52) = (b-B)'[(V_b-V_B)^(-1)](b-B) =   -30.11
chi2<0 ==> model fitted on these data fails to meet the asymptotic
assumptions of the Hausman test; see suest for a generalized test

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